Postscript — Eine kleine NASA-Tafel

Most of this stuff we don't need in the Fables but I've stuck it in here to have handy because it is not possible to predict what one might want to know in the course of making an imaginary trip. The metric units here are all OLD metric as contrasted with the new metric units described in the preface.

A NASA website gives the Keplerian attractiveness of the sun as 1.32712440018 × 1020meter3/second2. This is a shamelessly exquisite degree of precision but presumably one needs that many digits in order to navigate. This, or the equivalent in "astronomical units" is what is used for navigation. One does not use the kilogram mass of the sun, which is to say its inertia, and which is known only to four decimal places. Although the attractivness is known with exquisite precision the inertia is known with only mediocre accuracy because G, the ratio of attractiveness to inertia, is poorly known. G is only known to four or five places, hardly enough for navigation.

See the entry for the "heliocentric gravitational constant". I was very glad to see NASA listing the Keplerian attractiveness of the sun in metric units since they are more universal than "astronomical units" and more readily convertible to human-scale Planck units.

At the same site there are some mass ratios. When I say mass in this context I mean attractiveness instead of inertia because that is how the ratios were determined — not as ratios of inertias (which we do not know because we do not push heavenly bodies around to test their inertia) but as ratios of Keplerian attractivenesses (meter3/second2 quantities) which we tell for individual bodies by observing orbit behavior. The strict proportionality of inertia to attractiveness is not axiomatic but is something Dicke and others have attempted to verify. One cannot simply convert these ratios into inertia-ratios without comment.

Sun/(Earth+Moon) -----328900.56


If they were not navigating I would not believe this many digits. It would seem like an inflated claim to precision. But they are placing large bets on the accuracy.


Our Planck minutes are defined exactly as 20000/371 seconds and our paces are exactly 200/371 × 2.99792458 meters. (The metric number 299792458 is exact by definition of meter.) So we can make an exact conversion of the NASA "heliocentric gravitational constant" into our TPM units. I will leave off some digits because it would be embarrassing to write them all out.

9.1367857×1022 pace3/minute2
NASA says divide by 328900.56 to get the mass of earth and moon. And then it says multiply that by 81.30059/82.30059 to get earth's. Or else by 1/82.30059 to get the mass of the moon. All that stuff is based on the figure for the sun

Sun: 9.1367857 ×1022 pace3/minute2.
Earth+Moon: 2.77798 ×1017 pace3/minute2.
Earth: 2.74422 ×1017 pace3/minute2.
Moon: 3.37540 ×1015 pace3/minute2.

NASA data is public domain. Discussion copyright 2002 Leonard Cottrell.
Table of contents for the Mainstream Physics Fables